These are sample practice MCQs created for exam preparation. These are NOT official exam questions.
P can complete a project in 20 days. Q is 25% more efficient than P. If they work together for 6 days and then Q continues alone, how many more days will Q need to complete the project?
Question:
P can complete a project in 20 days. Q is 25% more efficient than P. If they work together for 6 days and then Q continues alone, how many more days will Q need to complete the project?
P can complete a project in 20 days. Q is 25% more efficient than P. If they work together for 6 days and then Q continues alone, how many more days will Q need to complete the project?
Options
Answer: (A) 5.2 days
Explanation:
P rate = 1/20 per day. Q rate = (1/20) × 1.25 = 1/16 per day. Together rate = 1/20 + 1/16 = 4/80 + 5/80 = 9/80 per day. Work done in 6 days = 6 × 9/80 = 54/80 = 27/40. Remaining = 1 - 27/40 = 13/40. Time for Q alone = (13/40)/(1/16) = (13/40) × 16 = 13 × 16/40 = 208/40 = 5.2 days.
Explanation:
P rate = 1/20 per day. Q rate = (1/20) × 1.25 = 1/16 per day. Together rate = 1/20 + 1/16 = 4/80 + 5/80 = 9/80 per day. Work done in 6 days = 6 × 9/80 = 54/80 = 27/40. Remaining = 1 - 27/40 = 13/40. Time for Q alone = (13/40)/(1/16) = (13/40) × 16 = 13 × 16/40 = 208/40 = 5.2 days.
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